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     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Brownian Motion\n",
      "===============\n",
      "\n",
      "*Brownian motion* is a stochastic process. One form of the equation for\n",
      "Brownian motion is\n",
      "\n",
      "$X(0)\u00a0=\u00a0X_0$\n",
      "\n",
      "$X(t\u00a0+\u00a0dt)\u00a0=\u00a0X(t)\u00a0+\u00a0N(0,\u00a0(delta)^2\u00a0dt;\u00a0t,\u00a0t+dt)$\n",
      "\n",
      "where $N(a, b; t_1, t_2)$ is a normally distributed random\n",
      "variable with mean a and variance b. The parameters $t_1$ and $t_2$\n",
      "make explicit the statistical independence of *N* on different time\n",
      "intervals; that is, if $[t_1, t_2)$ and $[t_3, t_4)$ are\n",
      "disjoint intervals, then $N(a, b; t_1, t_2)$ and $N(a, b; t_3,\n",
      "t_4)$ are independent.\n",
      "\n",
      "The calculation is actually very simple. A naive implementation that\n",
      "prints *n* steps of the Brownian motion might look like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import norm\n",
      "\n",
      "# Process parameters\n",
      "delta = 0.25\n",
      "dt = 0.1\n",
      "\n",
      "# Initial condition.\n",
      "x = 0.0\n",
      "\n",
      "# Number of iterations to compute.\n",
      "n = 20\n",
      "\n",
      "# Iterate to compute the steps of the Brownian motion.\n",
      "for k in range(n):\n",
      "    x = x + norm.rvs(scale=delta**2*dt)\n",
      "    print x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.0149783802189\n",
        "0.0153383445186\n",
        "0.0234318982959\n",
        "0.0212808305024\n",
        "0.0114258184942\n",
        "0.01354252966\n",
        "0.024915691657\n",
        "0.0225717389674\n",
        "0.0202001899576\n",
        "0.0210395736257\n",
        "0.0346234119557\n",
        "0.0315723937897\n",
        "0.0296012566384\n",
        "0.0296135943506\n",
        "0.0198499273499\n",
        "0.0165205162055\n",
        "0.00688369775327\n",
        "0.0069949507719\n",
        "0.00888200058681\n",
        "0.00297662267152\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above code could be easily modified to save the iterations in an\n",
      "array instead of printing them.\n",
      "\n",
      "The problem with the above code is that it is slow. If we want to\n",
      "compute a large number of iterations, we can do much better. The key is\n",
      "to note that the calculation is the cumulative sum of samples from the\n",
      "normal distribution. A fast version can be implemented by first\n",
      "generating all the samples from the normal distribution with one call to\n",
      "scipy.stats.norm.rvs(), and then using the numpy *cumsum* function to\n",
      "form the cumulative sum.\n",
      "\n",
      "The following function uses this idea to implement the function\n",
      "*brownian()*. The function allows the initial condition to be an array\n",
      "(or anything that can be converted to an array). Each element of *x0* is\n",
      "treated as an initial condition for a Brownian motion."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\"\"\"\n",
      "brownian() implements one dimensional Brownian motion (i.e. the Wiener process).\n",
      "\"\"\"\n",
      "\n",
      "# File: brownian.py\n",
      "\n",
      "from math import sqrt\n",
      "from scipy.stats import norm\n",
      "import numpy as np\n",
      "\n",
      "\n",
      "def brownian(x0, n, dt, delta, out=None):\n",
      "    \"\"\"\n",
      "    Generate an instance of Brownian motion (i.e. the Wiener process):\n",
      "\n",
      "        X(t) = X(0) + N(0, delta**2 * t; 0, t)\n",
      "\n",
      "    where N(a,b; t0, t1) is a normally distributed random variable with mean a and\n",
      "    variance b.  The parameters t0 and t1 make explicit the statistical\n",
      "    independence of N on different time intervals; that is, if [t0, t1) and\n",
      "    [t2, t3) are disjoint intervals, then N(a, b; t0, t1) and N(a, b; t2, t3)\n",
      "    are independent.\n",
      "    \n",
      "    Written as an iteration scheme,\n",
      "\n",
      "        X(t + dt) = X(t) + N(0, delta**2 * dt; t, t+dt)\n",
      "\n",
      "\n",
      "    If `x0` is an array (or array-like), each value in `x0` is treated as\n",
      "    an initial condition, and the value returned is a numpy array with one\n",
      "    more dimension than `x0`.\n",
      "\n",
      "    Arguments\n",
      "    ---------\n",
      "    x0 : float or numpy array (or something that can be converted to a numpy array\n",
      "         using numpy.asarray(x0)).\n",
      "        The initial condition(s) (i.e. position(s)) of the Brownian motion.\n",
      "    n : int\n",
      "        The number of steps to take.\n",
      "    dt : float\n",
      "        The time step.\n",
      "    delta : float\n",
      "        delta determines the \"speed\" of the Brownian motion.  The random variable\n",
      "        of the position at time t, X(t), has a normal distribution whose mean is\n",
      "        the position at time t=0 and whose variance is delta**2*t.\n",
      "    out : numpy array or None\n",
      "        If `out` is not None, it specifies the array in which to put the\n",
      "        result.  If `out` is None, a new numpy array is created and returned.\n",
      "\n",
      "    Returns\n",
      "    -------\n",
      "    A numpy array of floats with shape `x0.shape + (n,)`.\n",
      "    \n",
      "    Note that the initial value `x0` is not included in the returned array.\n",
      "    \"\"\"\n",
      "\n",
      "    x0 = np.asarray(x0)\n",
      "\n",
      "    # For each element of x0, generate a sample of n numbers from a\n",
      "    # normal distribution.\n",
      "    r = norm.rvs(size=x0.shape + (n,), scale=delta*sqrt(dt))\n",
      "\n",
      "    # If `out` was not given, create an output array.\n",
      "    if out is None:\n",
      "        out = np.empty(r.shape)\n",
      "\n",
      "    # This computes the Brownian motion by forming the cumulative sum of\n",
      "    # the random samples. \n",
      "    np.cumsum(r, axis=-1, out=out)\n",
      "\n",
      "    # Add the initial condition.\n",
      "    out += np.expand_dims(x0, axis=-1)\n",
      "\n",
      "    return out"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Example\n",
      "\n",
      "Here's a script that uses this function and matplotlib's pylab module to\n",
      "plot several realizations of Brownian motion."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy\n",
      "from pylab import plot, show, grid, xlabel, ylabel\n",
      "\n",
      "# The Wiener process parameter.\n",
      "delta = 2\n",
      "# Total time.\n",
      "T = 10.0\n",
      "# Number of steps.\n",
      "N = 500\n",
      "# Time step size\n",
      "dt = T/N\n",
      "# Number of realizations to generate.\n",
      "m = 20\n",
      "# Create an empty array to store the realizations.\n",
      "x = numpy.empty((m,N+1))\n",
      "# Initial values of x.\n",
      "x[:, 0] = 50\n",
      "\n",
      "brownian(x[:,0], N, dt, delta, out=x[:,1:])\n",
      "\n",
      "t = numpy.linspace(0.0, N*dt, N+1)\n",
      "for k in range(m):\n",
      "    plot(t, x[k])\n",
      "xlabel('t', fontsize=16)\n",
      "ylabel('x', fontsize=16)\n",
      "grid(True)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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cXDljxuiwsrLvFr8XsxkqKsKZOxfCwyN4912IjAxn715Yty6CggLw9+94fz4+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uaZFjMSLiYgPgolTS7HBQNaCUQ+oazEtDuf9+uWhwnjGQ3VRBeroMNq5bJ6+l1YZwsi6Thc0D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\nZvP000/z1ltvYWHRZr6uZpGamoqnpyfTp08nJiaGBx9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       "text": [
        "<matplotlib.figure.Figure at 0x4843d50>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 2D Brownian Motion\n",
      "\n",
      "The same function can be used to generate Brownian motion in two\n",
      "dimensions, since each dimension is just a one-dimensional Brownian\n",
      "motion.\n",
      "\n",
      "The following script provides a demo."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy\n",
      "from pylab import plot, show, grid, axis, xlabel, ylabel, title\n",
      "\n",
      "# The Wiener process parameter.\n",
      "delta = 0.25\n",
      "# Total time.\n",
      "T = 10.0\n",
      "# Number of steps.\n",
      "N = 500\n",
      "# Time step size\n",
      "dt = T/N\n",
      "# Initial values of x.\n",
      "x = numpy.empty((2,N+1))\n",
      "x[:, 0] = 0.0\n",
      "\n",
      "brownian(x[:,0], N, dt, delta, out=x[:,1:])\n",
      "\n",
      "# Plot the 2D trajectory.\n",
      "plot(x[0],x[1])\n",
      "    \n",
      "# Mark the start and end points.\n",
      "plot(x[0,0],x[1,0], 'go')\n",
      "plot(x[0,-1], x[1,-1], 'ro')\n",
      "\n",
      "# More plot decorations.\n",
      "title('2D Brownian Motion')\n",
      "xlabel('x', fontsize=16)\n",
      "ylabel('y', fontsize=16)\n",
      "axis('equal')\n",
      "grid(True)\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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t2/NXENeu0f3XxYWeWr/8krMEB6AXHACN6fb2abdNTgY2bgRq1VLxInkFpbbK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\ndevWhffTUFzdBye3bgc8LeKQU/pj6e1fftHi5k2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       "text": [
        "<matplotlib.figure.Figure at 0x486f310>"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}